2017/01/16 by Svjetlana Terzić, Svjetlana Terzic, Terzic, Svjetlana
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math.DG #msc:53C25 #msc:53C30
paper · pdf · doi:10.48550/arxiv.1701.04479
Lemma 1 clarified and exposition improved, to appear in the Proceedings of XIX Geometrical Seminar as a special volume of Publications de l'Institute Mathematique (Beograd)
arxiv created 2017/10/01 · arxiv updated 2017/10/03
We discuss the question of geometric formality for rationally elliptic manifolds of dimension 6 and 7. We prove that a geometrically formal six-dimensional biquotient with b2=3 has the real cohomology of a symmetric space. We also show that a rationally hyperbolic six-dimensional manifold with b2≤ 2 and b3=0 can not be geometrically formal. As it follows from their real homotopy classification, the seven-dimensional geometrically formal rationally elliptic manifolds have the real cohomology of symmetric spaces as well.